Are all breakthroughs in AI and machine learning are due to increase in computational resources?
High-level answer: Increase in resources has been important in AI, and definitely was a factor with Deep Blue, but Machine Learning is a newer method that seems to produces more optimal results with less resources on problems of greater complexity.  

Here is an article on AlphaGo's hardware: "Google reveals the mysterious custom hardware that powers AlphaGo"

Also an interesting analysis on Quora: "What hardware does AlphaGo run on? Is it customized hardware for best performance?"

Still pretty powerful systems, but I think the algorithms are as important as the computing resources, because all the hardware in the world won't help in the algorithms are poor. 

Matthew Lai, creator of Giraffe Chess, said:


  "In the ensuing two decades [since Deep Blue], both computer hardware and AI research advanced the state-of-art chess-playing computers to the point where even the best humans today have no realistic chance of defeating a modern chess engine running on a smartphone."Source: TechExplore


which suggests that hardware and software are both important parts of the overall equation.